Another vote for NLCS here. My DD was a 7+ intake, and the sensitive sort. She is thriving there. We were in a sort of similar position to you when we made our choice as she had been accepted by other schools e.g SHHS, City etc and we had doubts but eventually her love for NLCS and the academics was the decising factor for us. You are right that the ethnic mix is completely different in these 2 schools. Highgate is mainly white Christian/Jewish. In my DD's class 50%-60% is Asian with a sprinkle of everything else. They all mix fine though. There is a mixture of personalities, from the overconfident to the quiet ones. If anything I find that the quieter ones eventually get out of their shell and they are doing fine. Girls' friendships are always a tricky thing so if your DD is the sensitive sort who does not like disharmony she will face the same challenges wherever she goes, even at a co-ed school. At primary level girls tend to play together and being at a co-ed school doesn't change this. My DD was at a co-ed prep school before and friendship or disharmony issues were no different. If anything at NLCS it is easier to walk away and play with someone else as both classes (all 50 girls) play together, the girls have joint parties and generally do things together.
NLCS is also far more academic than Highgate and as horsemadmom said there is no gender bias towards subjects. My DD loves science and they do a lot of it in a fun way. They also do chess as part of the normal curriculum (in addition to any clubs). We do not feel any "pressure". The pace is fast and the girls have some sort of homework every day (e.g science, history, geography, maths) from the early days but nothing taxing. Some of it is research based so your DD will need to familiarise herself with internet research and encyclopedias so adult support is needed at least at first. They do teach them research skills at school though, which is great. The year 3 teachers and TAs are lovely.
Parental involvment at school events etc is no different to any other school. Not the schools that my kids attend anyway and there are working mums at NLCS who cannot help with the sewing of the Christmas concert costumes. That's fine. :-)
If memory serves right there will be an offer holders meeting soon. If in doubt speak to some of the existing mums. They are honest and helpful.
Lastly, as you will have guessed from my name we do not live local to the school. DD returns to our neck of the woods on the coach around 5, or 4.30 when she doesn't go to clubs and gets the early coach. We have not found it a problem (although I must admit that attending events is a little bit more of a hassle for us than if she attended a local school).
Apologies for the very long post (and any typos) I hope it was helpful. Good luck!